U.S. patent application number 10/200179 was filed with the patent office on 2003-01-23 for manipulator control method.
This patent application is currently assigned to Communications Res. Lab., Ind. Admin. Inst.. Invention is credited to Kimura, Shininchi.
Application Number | 20030018412 10/200179 |
Document ID | / |
Family ID | 19055477 |
Filed Date | 2003-01-23 |
United States Patent
Application |
20030018412 |
Kind Code |
A1 |
Kimura, Shininchi |
January 23, 2003 |
Manipulator control method
Abstract
A method for controlling a hyper-redundant manipulator including
a plurality of links coupled by joints by determining the shape the
manipulator takes when the end of the manipulator is moved to a
target position, includes modeling each link as an elastic body
having a natural length and a suitable modulus of elasticity that
enables the elastic body to stretch and contract, simulating the
overall shape of the manipulator when the end has been moved to the
target position with the joints locked at a freezed angle and the
joints are unlocked to return each link to its natural length, and
moving the manipulator end to the target position by controlling
each joint angle to match the simulation outcome.
Inventors: |
Kimura, Shininchi;
(Koganei-shi, JP) |
Correspondence
Address: |
OBLON SPIVAK MCCLELLAND MAIER & NEUSTADT PC
FOURTH FLOOR
1755 JEFFERSON DAVIS HIGHWAY
ARLINGTON
VA
22202
US
|
Assignee: |
Communications Res. Lab., Ind.
Admin. Inst.
Koganei-shi
JP
|
Family ID: |
19055477 |
Appl. No.: |
10/200179 |
Filed: |
July 23, 2002 |
Current U.S.
Class: |
700/245 |
Current CPC
Class: |
B25J 9/1605 20130101;
G05B 2219/39415 20130101; G05B 2219/40527 20130101; G05B 2219/39018
20130101 |
Class at
Publication: |
700/245 |
International
Class: |
G06F 019/00 |
Foreign Application Data
Date |
Code |
Application Number |
Jul 23, 2001 |
JP |
2001-221884 |
Claims
What is claimed is:
1. A method for controlling a hyper-redundant manipulator
comprising a plurality of links coupled by joints, by determining a
shape the manipulator forms from base to end when the end is moved
to a target position, the method comprising: modeling each link as
an elastic body having a natural length and an appropriate modulus
of elasticity that enables the elastic body to stretch and contract
just in a linkage direction; simulating an overall shape of the
manipulator when the end has been moved to a target position with
the joints locked at a freezed angle and the joints are unlocked to
return each link to its natural length; and moving the manipulator
end to the target position by controlling each joint angle to match
the simulation outcome.
2. The manipulator control method according to claim 1, wherein the
modulus of elasticity of the elastic body constituting each link
has a nonlinear characteristic.
3. The manipulator control method according to claim 1, wherein the
overall shape of the manipulator, when there is an obstacle to the
movement of the manipulator end to a target position, is determined
by introducing the obstacle as an external force acting on each
elastic body that is inversely proportional to a distance between
the obstacle and each elastic body.
4. The manipulator control method according to claim 2, wherein the
overall shape of the manipulator, when there is an obstacle to the
movement of the manipulator end to a target position, is determined
by introducing the obstacle as an external force acting on each
elastic body that is inversely proportional to a distance between
the obstacle and each elastic body.
5. The manipulator control method according to claim 1, wherein the
overall shape of the manipulator, when a joint is unable to
function, is determined by joining links on each side of the failed
joint to form a virtual link that is introduced as a virtual
elastic body that can stretch and contract along a straight line
that connects the ends of the virtual link that constitutes the
natural length thereof.
6. The manipulator control method according to claim 2, wherein the
overall shape of the manipulator, when a joint is unable to
function, is determined by joining links on each side of the failed
joint to form a virtual link that is introduced as a virtual
elastic body that can stretch and contract along a straight line
that connects the ends of the virtual link that constitutes the
natural length thereof.
7. The manipulator control method according to claim 3, wherein the
overall shape of the manipulator, when a joint is unable to
function, is determined by joining links on each side of the failed
joint to form a virtual link that is introduced as a virtual
elastic body that can stretch and contract along a straight line
that connects the ends of the virtual link that constitutes the
natural length thereof.
8. The manipulator control method according to claim 4, wherein the
overall shape of the manipulator, when a joint is unable to
function, is determined by joining links on each side of the failed
joint to form a virtual link that is introduced as a virtual
elastic body that can stretch and contract along a straight line
that connects the ends of the virtual link that constitutes the
natural length thereof.
9. The manipulator control method according to claim 1, wherein the
overall shape of the manipulator, when the manipulator is
selectively moved to a target position, is determined by using a
plurality of processing means to carry out a decentralized
simulation of the overall shape.
10. The manipulator control method according to claim 2, wherein
the overall shape of the manipulator, when the manipulator is
selectively moved to a target position, is determined by using a
plurality of processing means to carry out a decentralized
simulation of the overall shape.
11. The manipulator control method according to claim 3, wherein
the overall shape of the manipulator, when the manipulator is
selectively moved to a target position, is determined by using a
plurality of processing means to carry out a decentralized
simulation of the overall shape.
12. The manipulator control method according to claim 4, wherein
the overall shape of the manipulator, when the manipulator is
selectively moved to a target position, is determined by using a
plurality of processing means to carry out a decentralized
simulation of the overall shape.
13. The manipulator control method according to claim 5, wherein
the overall shape of the manipulator, when the manipulator is
selectively moved to a target position, is determined by using a
plurality of processing means to carry out a decentralized
simulation of the overall shape.
14. The manipulator control method according to claim 6, wherein
the overall shape of the manipulator, when the manipulator is
selectively moved to a target position, is determined by using a
plurality of processing means to carry out a decentralized
simulation of the overall shape.
15. The manipulator control method according to claim 7, wherein
the overall shape of the manipulator, when the manipulator is
selectively moved to a target position, is determined by using a
plurality of processing means to carry out a decentralized
simulation of the overall shape.
16. The manipulator control method according to claim 8, wherein
the overall shape of the manipulator, when the manipulator is
selectively moved to a target position, is determined by using a
plurality of processing means to carry out a decentralized
simulation of the overall shape.
Description
BACKGROUND OF THE INVENTION
[0001] 1. Field of the Invention
[0002] The present invention relates to a method for controlling an
industrial manipulator used for assembly, painting and operations
in a factory, or a space manipulator used for carrying out
inspections and assembly operations and the like in space. The
invention particularly relates to a method for effectively
controlling a hyper-redundant type manipulator having the degrees
of freedom exceeding the required degrees of freedom.
[0003] 2. Description of the Prior Art
[0004] In a manipulator in which a plurality of links are connected
by joints, the necessary angle that each joint must have in order
to move the manipulator tip to a target position is generally
calculated by making up a Jacobi matrix for calculating tip
displacement from the joint angle displacement, and using an
inverse Jacobi matrix corresponding to the inverse transformation
of the Jacobi matrix to find the joint angle values.
[0005] An inverse Jacobi matrix can be uniquely obtained with
respect to a manipulator in which the degrees of freedom are the
same as the required degrees of freedom. However, in the case of
hyper-redundant manipulators that have more than the necessary
degrees of freedom, it cannot be uniquely obtained because the
Jacobi matrix becomes a rectangular matrix. Therefore, what
designers have been doing is setting a number of constraint
conditions and using singular value analysis or Lagrange's
undetermined multiplier method or the like to calculate a pseudo
inverse matrix.
[0006] However, when the above method is used to control
hyper-redundant manipulators, the problem has been that as the
difference between the necessary degrees of freedom and the degrees
of freedom possessed by the manipulator increases, that is, as the
degree of redundancy increases, the calculations become
increasingly complex. In addition, it has been necessary to use
special calculations to adapt to partial failure of the
manipulator. It is also necessary to perform these calculations in
a centralized manner, which has not been suitable for the
distributed control structures that have been coming into general
use in recent years.
[0007] Considerable work is underway to develop hyper-redundant
manipulators that can move flexibly, avoid obstacles and cope with
partial failures. In particular, manipulators with high hyper
redundancy are being developed that when used for inspecting
satellites in orbit, are adept at getting around objects and can
continue to function even after suffering a partial failure. When
this type of space-based application is considered, the calculation
resources available for controlling the manipulator are highly
limited by the harshness of the environmental conditions, such as
radiation and extremely low temperatures. Therefore, there is a
limit when it comes to centralized computation of joint angle
values in the case of a manipulator having a high hyper redundancy.
Development is therefore focusing on getting around individual
constraints on computing resources by using processors to control
joints, a modular configuration and decentralized control to
achieve robustness with respect to failures. This being the case,
it is also desirable to be able to readily apply such a distributed
control structure as a way of determining manipulator joint
angles.
[0008] An object of the present invention is to provide a
manipulator control method that employs a technique of determining
angles of manipulator joints to control a manipulator using a
distributed control structure, that can be readily applied to
manipulators having a high degree of redundancy and to manipulators
that suffer failure.
SUMMARY OF THE INVENTION
[0009] To attain the above object, the present invention provides a
method for controlling a hyper-redundant manipulator comprising a
plurality of links coupled by joints, by determining a shape the
manipulator forms from base to end when the end is moved to a
target position, the method comprising: modeling each link as an
elastic body having a natural length and an appropriate modulus of
elasticity that enables the elastic body to stretch and contract
just in a linkage direction, simulating an overall shape of the
manipulator when the end has been moved to a target position with
the joints locked at a freezed angle and the joints are unlocked to
return each link to its natural length, and moving the manipulator
end to the target position by controlling each joint angle to match
the simulation outcome.
[0010] In the above manipulator control method, the modulus of
elasticity of the elastic body constituting each link has a
nonlinear characteristic.
[0011] In the method, when there is an obstacle to the movement of
the manipulator end to the target position, the overall shape of
the manipulator is determined by introducing the obstacle as an
external force acting on each elastic body that is inversely
proportional to a distance between the obstacle and each elastic
body.
[0012] In the method, when a joint is unable to function, the
overall shape of the manipulator is determined by connecting links
on each side of the failed joint to assume a virtual link that is
introduced as an assumed elastic body that can stretch and contract
along a straight line that connects the ends of the virtual link
and is treated as the natural length of the virtual link when the
joint has become unmovable.
[0013] In the method, when the manipulator is selectively moved to
a target position, the overall shape of the manipulator is
determined by using a plurality of processing means to carry out a
decentralized simulation of the overall shape.
[0014] With the manipulator control method of this invention, the
time-evolution of a spring with a given displacement can be found
by calculating the displacement produced in the spring,
facilitating the calculation and making the method applicable to
hyper-redundant manipulators. The time-evolution of a spring with a
given displacement can also be calculated from the spring
displacement and the external force at each end of the spring,
making it possible to realize manipulator control using a
decentralized control structure. The method can also be applied to
a faulty manipulator by introducing a virtual link that includes
the faulty joint.
[0015] Further features of the invention, its nature and various
advantages will be more apparent from the accompanying drawings and
following detailed description of the invention.
BRIEF DESCRIPTION OF THE DRAWINGS
[0016] FIG. 1(a) is a schematic diagram of a two-dimensional
manipulator.
[0017] FIG. 1(b) is a conceptual diagram of the manipulator of FIG.
1(a) modeled as a coupled spring system.
[0018] FIG. 2(a) is a schematic diagram of a two-dimensional
manipulator that has a faulty joint.
[0019] FIG. 2(b) is a conceptual diagram of the manipulator of FIG.
2(a) modeled as a coupled spring system.
[0020] FIG. 3(a) is a schematic diagram of a two-dimensional
manipulator with a nearby obstacle.
[0021] FIG. 3(b) is a conceptual diagram of the manipulator of FIG.
3(a) modeled as a coupled spring system.
[0022] FIG. 4(a) is a drawing of a two-dimensional manipulator with
five degrees of freedom modeled as a coupled spring, showing the
simulated manipulator shapes obtained when the end was moved to
each of four points.
[0023] FIG. 4(b) shows the changes in the stretch length of the
springs as the springs converge to their natural length with
respect to each of the end positions in FIG. 4(a).
[0024] FIG. 5(a) is a drawing of a two-dimensional manipulator with
ten degrees of freedom modeled as a coupled spring, showing the
simulated manipulator shapes obtained when the end was moved to
each of four points.
[0025] FIG. 5(b) shows the changes in the stretch length of the
springs as the springs converge to their natural length with
respect to each of the end positions in FIG. 5(a).
[0026] FIG. 6(a) is a drawing of a two-dimensional manipulator with
ten degrees of freedom modeled as a coupled spring having linear
characteristics, showing the simulated manipulator shapes obtained
when the end was moved to each of four points.
[0027] FIG. 6(b) shows the changes in the stretch length of the
springs as the springs converge to their natural length with
respect to each of the end positions in FIG. 6(a).
[0028] FIG. 7(a) is a drawing of a two-dimensional manipulator with
ten degrees of freedom modeled as a coupled spring having
excessively nonlinear characteristics, showing the simulated
manipulator shapes obtained when the end was moved to each of four
points.
[0029] FIG. 7(b) shows the changes in the stretch length of the
springs as the springs converge to their natural length with
respect to each of the end positions in FIG. 7(a).
DESCRIPTION OF THE PREFERRED EMBODIMENT
[0030] Before describing embodiments of the manipulator control
method of the present invention with reference to the accompanying
drawings and the method used to determine the joint angle will be
explained.
[0031] N springs are coupled together to form a coupled spring
system in which the natural length is the length of the links from
L1 to LN. In the absence of a continuous application of an external
force, the coupled spring system converges to a shape that
satisfies each of the lengths L1 to LN. It is assumed that the
springs do not bend or twist, but only stretch and contract
one-dimensionally. If the spring has a nonlinear characteristic,
the shape converges more swiftly than when the spring has a linear
characteristic.
[0032] The manipulator discussed here is the length of the N links
L1 to LN. The positions of the manipulator base and end effector
are freezed, with the angles of the joints that couple the springs
together in a non-changeable state. When the joints are then
allowed to bend, if the base to the end of the coupled spring are
within the extended total length (L1+L2+ . . . LN) of the springs,
by stretching or contracting, each spring will converge to a shape
that satisfies length L1 to LN. The shape at this time (the angles
of the joints) will be the shape of the manipulator that realizes
the target position.
[0033] Thus, unlike in the prior art in which the angles to which
the joints should be controlled are obtained directly, in the
method of this invention, the joint angles are determined by
simulating the shape obtained when the links constituted as elastic
bodies that have been longitudinally deformed to move the end to
the target position revert to their natural length, with the
manipulator being controlled by the degree of change in the joint
angles that accompanies the change in shape. Thus, if the overall
shape of the manipulator is known before moving the manipulator
end, it is possible to uniquely determine what the manipulator
shape will be after the end is moved.
[0034] Thus, unlike in the prior art method of determining
manipulator joint angles which requires that the manipulator shape,
faulty joints, obstacles and the like be introduced into an inverse
Jacobi matrix, in accordance with the method of the present
invention, the shape can be determined merely by simulating the
time-evolution of a spring having a given displacement,
facilitating the calculation process and making the method
applicable to manipulators having a high degree of hyper
redundancy. The time-evolution of a spring to which displacement is
applied can also be calculated from the displacement produced in
the spring and the external force at each end of the spring, making
it possible to readily realize a decentralized control structure by
using a plurality of processors to perform the necessary
calculations for determining the shape. This means that the method
can be used to calculate the shape of hyper-redundant manipulators,
even with the limited computing resources of computers used in
space.
[0035] FIG. 1 will now be used to describe an embodiment of the
present invention in which a coupled spring system is used to
simulate the above manipulator. For simplicity, the invention is
described with reference to its application to a two-dimensional
manipulator system. The algorithm is extremely simple, and can
therefore be readily extended to a three-dimensional system. It is
assumed that the manipulator is being used to inspect a satellite
in orbit, for which the task involves relative movement, from an
existing position, of an end effector of a manipulator in an
arbitrary initial state.
[0036] As shown in FIG. 1(a), manipulator 1 is formed as a movable
arm comprised of first and second links L1 and L2 coupled by joint
J1, second and third links L2 and L3 coupled by joint J2, third and
fourth links L3 and L4 coupled by joint J3, fourth and fifth links
L4 and L5 coupled by joint J4, fifth and sixth links L5 and L6
coupled by joint J5 and sixth and seventh links L6 and L7 coupled
by joint J6. The movable arm has a base 2 at the base end (the end
of the link L1 that is not attached to the joint J1) and an end
effector 3 at the other end (the end of the link L7 that is not
attached to the joint J6).
[0037] When this is modeled as a coupled spring, as shown in FIG.
1(b), the first link L1 is replaced by a first elastic body 41, the
second link L2 by a second elastic body 42, the third link L3 by a
third elastic body 43, the fourth link L4 by a fourth elastic body
44, the fifth link L5 by a fifth elastic body 45, the sixth link L6
by a sixth elastic body 46, and the seventh link L7 by a seventh
elastic body 47; joints J1 to J6 are assumed to be freezed. The
elastic bodies 41 to 47 are linked end to end, each functioning
like a coil spring that has a suitable modulus of elasticity and
can only stretch or contract in a straight line. The natural length
of each of the elastic bodies 41 to 47 is equal to the length of
the manipulator links L1 to L7.
[0038] The elastic function of the elastic bodies 41 to 47 is not
limited to that of a coil spring, but may instead be that of any
elastic material that can be modeled. In this embodiment, a spring
is used that is assumed to have a natural length L.sub.0 and
nonlinear viscoelastic properties at a spring length L at a given
instant. The spring dynamic is 1 2 L t 2 = K 1 ( L - L 0 ) j + K 2
( L - L 0 ) + D L t ( 1 )
[0039] where K.sub.1 is the modulus of elasticity of the nonlinear
component, K.sub.2 is the modulus of elasticity of the linear
component, and D is the coefficient of friction produced by the
movement of the spring. These parameters can be set to reproduce
the desired physical properties in the elastic bodies. Coefficient
of friction D is introduced as one of the parameters since the
energy imparted by the elastic spring displacement is gradually
released by the frictional effect as the spring converges to its
natural length.
[0040] When a command is issued to effect relative movement of the
end effector 3, simulations are carried out with the other parts of
the coupled spring system (joints J1 to J6 and the coupling between
base 2 and link L1) being freezed as the end is displaced in the
specified direction, in which state the overall spring is released,
with the simulation continuing until the coupled spring reaches a
steady state, and the angle of curvature of the spring when the
displacement goes below a certain value is indicated as the joint
angle (since in the case of a nonlinear spring the oscillations can
be quite pronounced, and it is inefficient to continue the
simulation until the spring has come to a complete stop). Proper
control of the manipulator 1 can be speedily achieved using
calculations that impose only a small load on processors.
[0041] The number of calculation cycles required for the spring to
converge to the natural length depends on the size of the
displacement. In the case of a displacement in the order of 10 mm,
100 cycles are enough to achieve sufficient convergence. If there
is enough processing capability for that, simulations for
determining the joint angles can be performed with no problem.
Therefore, by providing each link with its own calculation
processing means, a decentralized processing system can be readily
configured.
[0042] When the manipulator includes a faulty (freezed) joint, the
manipulator can be modeled by introducing a powerful nonlinear
spring having as its natural length the length of the links
preceding and following the faulty joint. Specifically, as shown in
FIG. 2(a), when the fourth joint J4 develops a fault that locks the
joint angle so it cannot be controlled, the links on either side,
links L4 and L5, are combined to form a virtual link L4-5
connecting joint J3 and joint J5.
[0043] FIG. 2(b) shows a manipulator that includes the virtual link
L4-5 modeled as a coupled spring. The difference from FIG. 1(b) is
that the fourth elastic body 44, fourth joint J4 and fifth elastic
body 45 are handled as being constituted by virtual elastic body
4V. Thus, the virtual elastic body 4V, corresponding to the virtual
link L4-5, has a natural length that is the straight-line distance
between the two ends of the virtual link L4-5 (from the end
connected to joint J3 to the end connected to joint J5), and can
stretch and contract along the line connecting the two ends of the
virtual link L4-5. This being the case, the same method described
above can be used to determine the angles of joints J1, J2, J3, J5
and J6 corresponding to the position to which the end effector 3 is
moved. When there is a plurality of faulty joints, each can be
modeled as a virtual elastic body. When there is a continuous
succession of faulty joints, virtual elastic bodies can be
introduced at each end of the drivable joints adjacent to the
faulty joints.
[0044] With respect to controlling a manipulator in which the joint
angles are limited owing to such factors as the physical structure
of the joints and the like, the same functionality can be achieved
by introducing a nonlinear spring connected to each side of the
joints concerned. Joint angle limitations can be expressed by
setting elastic body characteristics such as that the body produces
no force when stretched above a certain length, or which produces a
sudden counterforce when compressed by more than a certain amount,
to prevent the joint being bent more when it is near its limit
angle.
[0045] Also, when determining joint angles to operate a manipulator
while avoiding an obstacle, the post-deformation shape of the
manipulator can be simulated by introducing the obstacle as an
outside force acting on the elastic bodies that is inversely
proportional to the distance to the elastic bodies. A specific
example is shown in FIG. 3(a), where there is an obstacle 5 in the
vicinity of the manipulator. In this case, a shape can be
calculated that ensures the manipulator maintains at least a given
distance from the obstacle 5, by assuming virtual external forces
5V1 to 5V3 linking the position of the obstacle 5 with each of the
joints concerned, as shown in FIG. 3(b), for example the joints J3
to J5 that are near the obstacle 5. External forces from the
obstacle 5 that act on all the joints can be simulated. However,
with external forces being inversely proportional to the distance
involved, it is pointless to include in the calculations an
external force on joints that will be substantially unaffected by
the force. An external-force threshold value should therefore be
set, and only the external force acting on a joint that exceeds the
threshold should be calculated.
[0046] FIG. 4 shows the shape and the stretch time of each spring
when the algorithm is applied to a two-dimensional manipulator that
is 500 mm long and has five degrees of freedom, when the end was
moved relatively 20 mm up, down, left, and right from an initial
condition at which all joints were at an angle of 30 degrees. For
this simulation, with the natural length L.sub.0 of the nonlinear
spring set at 10, the parameters were set as K.sub.1=1000,
K.sub.2=0 and D=10. FIG. 4(a) shows line drawings of the converged
shapes of the coupled spring when the manipulator end effector was
moved backwards, forwards, left and right. These are the results of
calculations by the control method of this invention. FIG. 4(b)
shows time-based changes in the stretch length of each spring
during this process. It can be seen that the spring stretch length
rapidly decreased after the end effector was moved, converging to a
stretch length of zero, meaning the natural length. This shows that
with the control method of this invention, the resultant shape was
derived very speedily.
[0047] FIG. 4(b) shows when the manipulator end effector was moved
forward 20 mm at calculation cycle 101. Here, the spring
displacement more or less fully converges within 60 calculation
cycles. When the end effector was moved 20 mm back at calculation
cycle 201, 20 mm up at calculation cycle 301 and 20 mm down at
calculation cycle 401, in each case the stretch length converged
within 60 calculation cycles.
[0048] With respect to FIG. 5(a), the number of modules was
increased and the same algorithm used to simulate a two-dimensional
manipulator with ten degrees of freedom as a coupled spring; the
drawing shows the simulated manipulator shapes obtained when the
end effector was moved to each of four positions. FIG. 5(b) shows
the changes in the stretch length of the springs as the springs
converge to their natural length with respect to each of the end
effector positions shown in FIG. 5(a). It can be seen that despite
the increase in the degrees of freedom, algorithm operation was
just as stable.
[0049] FIGS. 6 and 7 depict a two-dimensional manipulator with ten
degrees of freedom with nonlinear spring constants K.sub.1 and
K.sub.2, modeled as a coupled spring with linear characteristics in
the case of FIG. 6, and modeled as a coupled spring with
excessively nonlinear characteristics in the case of FIG. 7,
showing the effect that spring nonlinearity has on the result. A
comparison of the two figures shows that convergence to a steady
state is faster in the case of a nonlinear spring. On the other
hand, it was confirmed that when the nonlinearity is excessive, the
displacement gives rise to strong vibrations and localized bending
readily occurs. There is no particular limitation with respect to
the modulus of elasticity to use for the simulated elastic bodies,
and whether to use linear or nonlinear characteristics, which are
options that come within the purview of design expertise.
[0050] As has been described in the foregoing, in accordance with
the manipulator control method of the present invention, the
manipulator shape can be determined merely by simulating the
time-evolution of a spring with a given displacement, unlike in the
prior art method in which the manipulator shape has to be
introduced into an inverse Jacobi matrix. This facilitates
calculations, which makes the method particularly effective in the
case of manipulators having a high degree of redundancy. Moreover,
the time-evolution of a spring that is displaced can also be
calculated from the spring displacement, making it easy to realize
a decentralized control configuration by using a plurality of
processors to perform the necessary calculations for the shape
determination. This means that the method can be used to calculate
the shape of hyper-redundant manipulators even with the limited
computing resources of computers used in space.
[0051] The elastic bodies used in accordance with the method can be
given nonlinear characteristics, resulting in speedy convergence to
their natural length and also reducing the number of calculation
cycles required to obtain a simulation result. The control method
can also be applied to shape-specific simulations by using the
introduction of obstacles as external forces acting on the elastic
bodies to obtain changes in joint angles accompanying the movement
of the manipulator end effector to a target position.
[0052] The method can also be applied to shape-specific simulations
in the case of a faulty manipulator by introducing a virtual link
that includes the faulty joint or joints to obtain changes in joint
angles accompanying the movement of the manipulator end effector to
a target position, without using the special calculations that have
to be employed in the prior art, and without having to perform the
calculations in a centralized manner. Shape-specific simulations
can also be carried out in a decentralized manner by using a
plurality of processors, making it possible to configure a
manipulator control system using relatively low-power CPUs disposed
at each link.
* * * * *